Question

7. A fluid flows past a sphere with an upstream velocity of Vo = 40 m/s as shown in the figure below. From a more advanced theory, it is found that the speed of the fluid along the front part of the sphere is V = (3/2)Vo sin 0. 40° VO, - r oka (a) Determine the streamwise and normal components of the acceleration at point A if the radius of the sphere is a = 0.20 m. (b) Find the location on the sphere where the velocity V is equal to zero. (This is called the stagnation point.) Compute the streamwise and normal components of the acceleration at the stagnation point.

Answer 1

Anwen Griven that, Upstream Velocity Vo = 40 mis Vo Speed of the fluid along front part of Sphere is Vavo sine, a = 0120 a) Determination of Streamuise and normal componerils of acceleration at A: Staramwise acceleration is is Normal Component of acceleration is As = vi ser (: 5-ao an = n (R=0) Substitute equation VR Substitute v an (312 vosine) an - - Ž vodine. Lo (3hvesine) la - Vo Sine. Vo coso a as su võ sino.cose — (1) an = 9 vo sino - (2) Substituete a, o,y values Substitute ao an = 9x45x Bin 40° L 4X012 4(0.2) (40) Sin 40 cos 40° an = 11.25x 1600 x 8740 an = 7437.166 mis 9x1600 Sin 40.coS40 0.8 as = 8863.269 mis .; Normal component of acceleration is 7437. 166 mis Streamwise acceleration is 8863.269 m/s b) Pind Jocation on the Sphere where v=0? Veo Ź yo sino = 0 sino - then 3/2 Vo Sino = 0 if Sino =0 when 0 = 0, TT V=0 when 0 = 0, TT

Compute as, an :- at o=0 Sin 8=0 Forom o as = 9 vosinco) cos() as=0 Forom @ = anze a vă since) an = 0. at ort =Sin T = 0 From O as = a Vo Sin (I) as=o From an võ sin (IT) an -0.